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If e^y(x+1)=1, prove that (d^2y)/(dx^2)=...

If `e^y(x+1)=1`, prove that `(d^2y)/(dx^2)=((dy)/(dx))^2`

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If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

If e^(y)(x+1)=1 , show that (d^(2)y)/(dx^(2)) = ((dy)/(dx))^(2) .

If ye^(y)=x , prove that, (dy)/(dx)=(y)/(x(1+y)) .

If y=xlog (x/(a+bx)) , prove that x^3(d^2y)/(dx^2)=(y-xdy/dx)^2 .

If y=sin^(-1) x, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0

If y= 3e^(2x)+2e^(3x) , prove that (d^(2)y)/(dx^(2))-5(dy)/(dx)+6y=0 .

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If ye^y=x prove that (dy)/(dx)= y/(x(1+y))

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. If y=e^(x+e^(x+e^(x+....TOoo))) prove that dy/dx=y/((1-y))

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  2. Differentiate tan ^(-1)((sqrt(1+x^2 )-1)/x) w,r,t. tan ^(-1)x

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  3. If e^y(x+1)=1, prove that (d^2y)/(dx^2)=((dy)/(dx))^2

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  4. If y=sin^(-1) x, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0

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  5. If x=a(theta+sin theta) and y=a(1-costheta), find (d^2y)/(dx^2)"at"the...

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  6. A particle moves along the curve y=2/3x^3. Find the points on the curv...

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  7. A man of height 1.6m, walks at a rate of 30m/sec away from a lamp whic...

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  8. Water is leaking from a conical funnel at the rate of 5cm^3//sec. If t...

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  9. Find the approximate value of log(10)10.1 it being given that log10e=0...

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  10. The time T of of oscillation of a simple pendulum of length l is given...

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  11. If in a triangle ABC, the side c and the angle C remain constant while...

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  12. Find the interval in which f(x)=2x^3+3x^2-12x+1 is increasing.

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  13. Find the interval in which f(x)=x^3-3x^2-9x+30 is strictly increasing ...

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  14. The function f(x)=sin^4x+cos^4x increasing if :

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  15. Let f(x)=int0^xe^t(t-1)(t-2)dt, Then f decreases in the interval

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  16. If f(x)=x.e^(x(1-x)), then f(x) is

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  17. Let f(x)=3x+5 then show f(x) is strictly increasing and f^(-1)(x) exis...

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  18. If alt0, and f(x)=e^(ax)+e^(-ax) Is monotonically decreasing. Find the...

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  19. If f''(x)gt0 and f'(1)=0 such that g(x)=f(cot^2x+2cotx+2), where 0ltxl...

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  20. Using calculus find the order relation between x and tan^(-1) x when "...

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